Scanning projector with non-rectangular display

ABSTRACT

A scanning beam projection system includes a scanning mirror having a fast-scan axis and a slow-scan axis. Movement on the fast-scan axis is controlled by a fast-scan scanning mirror control system. The control system receives position information describing angular displacement of the mirror. A fast-scan drive signal is generated that causes the scanning mirror to oscillate at a resonant frequency with a varying amplitude.

FIELD

The present invention relates generally to scanning beam displaysystems, and more specifically to controlling the deflection of scanningmirrors in scanning beam display systems.

BACKGROUND

Scanned light beams are used to produce display images for a widevariety of applications, including such applications as mobilemicroprojectors, automotive head-up displays, and head-worn displays.The displays are created by using the angular motion of a mirror todeflect a modulated light beam to cover the desired field of view. Bymoving the mirror about two orthogonal axes, a rectangular field of viewcan be created, providing the familiar look of a raster display in acompact and portable package.

Controlling the mirror deflection to correctly produce the desiredangular motion presents a significant engineering challenge.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a scanned beam projection system in accordance with variousembodiments of the present invention;

FIG. 2 shows beam deflection waveforms that result in the scantrajectory of FIG. 1;

FIG. 3 shows a plan view of a scanning platform with amicroelectromechanical system (MEMS) scanning mirror;

FIG. 4 shows a scanning mirror fast-scan control loop with a fast-scanamplitude drive circuit;

FIG. 5 shows a fast-scan oscillation drive circuit;

FIG. 6 shows a fast-scan amplitude drive circuit;

FIG. 7 shows an LMS tone adder;

FIG. 8 shows a fast-scan amplitude drive circuit using a harmoniccoefficient weighting array;

FIG. 9 shows an LMS tone adder using harmonic coefficient weighting;

FIG. 10 shows a fast-scan amplitude drive circuit that iterativelydetermines harmonic coefficients using a harmonic coefficient weightingarray;

FIG. 11 shows a fast-scan amplitude drive circuit that iterativelydetermines harmonic coefficients using an approximation of Newton'smethod;

FIG. 12 shows a scanning mirror fast-scan control loop with a fast-scansideband generator circuit;

FIG. 13 shows a fast-scan sideband generator circuit;

FIG. 14 shows a scanning mirror control loop that includes a digitalsignal processor;

FIG. 15 shows a block diagram of a mobile device in accordance withvarious embodiments of the present invention;

FIG. 16 shows a mobile device in accordance with various embodiments ofthe present invention;

FIG. 17 shows a head-up display system in accordance with variousembodiments of the invention; and

FIG. 18 shows eyewear in accordance with various embodiments of theinvention.

DESCRIPTION OF EMBODIMENTS

In the following detailed description, reference is made to theaccompanying drawings that show, by way of illustration, specificembodiments in which the invention may be practiced. These embodimentsare described in sufficient detail to enable those skilled in the art topractice the invention. It is to be understood that the variousembodiments of the invention, although different, are not necessarilymutually exclusive. For example, a particular feature, structure, orcharacteristic described herein in connection with one embodiment may beimplemented within other embodiments without departing from the scope ofthe invention. In addition, it is to be understood that the location orarrangement of individual elements within each disclosed embodiment maybe modified without departing from the scope of the invention. Thefollowing detailed description is, therefore, not to be taken in alimiting sense, and the scope of the present invention is defined onlyby the appended claims, appropriately interpreted, along with the fullrange of equivalents to which the claims are entitled. In the drawings,like numerals refer to the same or similar functionality throughout theseveral views.

FIG. 1 shows a scanned beam projection system in accordance with variousembodiments of the present invention. As shown in FIG. 1, scanned beamprojection system 100 includes a light source 110, which may be a laserlight source such as a laser diode or the like, capable of emitting abeam 112 which may be a laser beam. The beam 112 impinges on a scanningplatform 114 which includes a microelectromechanical system (MEMS) basedscanner or the like, and reflects off of scanning mirror 116 to generatea controlled output beam 124. A scanning mirror control circuit 130provides one or more drive signal(s) to control the angular motion ofscanning mirror 116 to cause output beam 124 to generate a raster scan126 on a projection surface 128.

In some embodiments, raster scan 126 is formed by combining a sinusoidalcomponent on the fast-scan axis (horizontal axis) and a sawtoothcomponent on the slow-scan axis (vertical axis). In these embodiments,controlled output beam 124 sweeps back and forth left-to-right in asinusoidal pattern, and sweeps vertically (top-to-bottom) in a sawtoothpattern with the display blanked during flyback (bottom-to-top). FIG. 1shows the fast-scan sinusoidal pattern as the beam sweeps verticallytop-to-bottom, but does not show the flyback from bottom-to-top.

In some embodiments, the sinusoidal component on the fast-scan axis hasa non-uniform amplitude. For example, as shown in FIG. 1, as thecontrolled output beam 124 sweeps vertically, the amplitude on thefast-scan axis changes. The fast-scan amplitude may change substantiallylinearly for a period of time as shown in FIG. 1, or may change in anymanner, including non-linearly. The varying fast-scan amplitude resultsin a non-rectangular display shape. For example, when the amplitudechanges linearly as shown in FIG. 1, the shape of the resulting displayis trapezoidal. This may be useful to pre-distort an image to match anangular projection surface 128; for example, when projection system 100is mounted on a ceiling and projecting on a wall.

Scanning mirror 116 is deflected according to signals provided byscanning mirror control circuit 130, and mirror position information isprovided back to scanning mirror control circuit 130 at 134. The mirrorposition information may describe angular position in the verticalslow-scan direction, the horizontal fast-scan direction, or both.Scanning mirror control circuit 130 receives the position information,determines the appropriate drive signals, and drives scanning mirror116.

FIG. 2 shows beam deflection waveforms that result in the raster scantrajectory of FIG. 1. Vertical deflection waveform 210 is a sawtoothwaveform, and horizontal deflection waveform 220 is a sinusoidalwaveform. The sawtooth vertical deflection waveform 210 includes afalling portion corresponding to the sweep of raster scan 126 fromtop-to-bottom, and also includes a rising portion corresponding to theflyback from bottom-to-top. After the flyback, the vertical sweeptraverses substantially the same path on each trajectory.

The amplitude 222 of the fast-scan deflection waveform 220 is shownlinearly decreasing during each vertical sweep. This results in thetrapezoidal display shape shown in FIG. 1. Amplitude 222 varies for afinite time period during each slow-scan sweep, and then repeats. Thefundamental frequency of the fast-scan amplitude variations is the sameas vertical deflection waveform 210. For example, in systems thatretrace on the slow-scan axis at 60 Hz, the fundamental frequency ofamplitude signal 222 is also 60 Hz.

It is important to note that the waveforms of FIG. 2 represent thedesired mirror deflection as opposed to the drive signals provided tothe scanning mirror. If the scanning mirror had a perfectly flat naturalresponse with no resonance, scanning mirror control circuit 130 coulddrive signals 210 and 220 as shown. In actual implementations, scanningmirror 116 has resonant characteristics with multiple distinct vibrationmodes. Scanning mirror control circuit 130 modifies the drive signals inan attempt to cause the scanning mirror 116 to deflect according to thewaveforms shown in FIG. 2 and thereby sweep controlled beam 124 togenerate raster scan 126.

For ease of illustration, FIGS. 1 and 2 show a relatively small numberof fast-scan cycles for each slow-scan cycle. In some embodiments, asignificantly larger number of fast-scan cycles exist for each slow-scancycle. For example, the slow-scan sweep may operate near 60 Hz and thefast-scan sweep may operate upwards of 18 kHz. One skilled in the artwill appreciate that the various embodiments of the present inventionmay be advantageously applied to any scanning system regardless of therelationship between slow and fast-scan frequencies.

Although FIGS. 1 and 2 show a sawtooth waveform for the slow-scandeflection, the various embodiments of the invention are not so limited.For example, the slow-scan deflection waveform may be triangular,limited harmonic sinusoidal, or any other shape, without departing fromthe scope of the present invention.

FIG. 3 shows a plan view of a scanning platform with amicroelectromechanical system (MEMS) scanning mirror. Scanning platform114 includes gimbal 340 and scanning mirror 116. Gimbal 340 is coupledto scanning platform 114 by flexures 310 and 312, and scanning mirror116 is coupled to gimbal 340 by flexures 320 and 322. Gimbal 340 has adrive coil connected to drive lines 350. Current driven into drive lines350 produces a current in the drive coil. Scanning platform 114 alsoincorporates one or more integrated piezoresistive position sensors. Insome embodiments, scanning platform 114 includes one position sensor foreach axis. Two of the interconnects 360 are coupled to drive lines 350.The remaining interconnects provide for the integrated position sensorsfor each axis.

In operation, an external magnetic field source (not shown) imposes amagnetic field on the drive coil. The magnetic field imposed on thedrive coil by the external magnetic field source has a component in theplane of the coil, and is oriented at roughly 45° with respect to thetwo drive axes. The in-plane current in the coil windings interacts withthe in-plane magnetic field to produce out-of-plane Lorentz forces onthe conductors. Since the drive current forms a loop on gimbal 340, thecurrent reverses sign across the scan axes. This means the Lorentzforces also reverse sign across the scan axes, resulting in a torque inthe plane of and normal to the magnetic field. This combined torqueproduces responses in the two scan directions depending on the frequencycontent of the torque.

The frequency components of the applied torque are selected to excitethe horizontal mirror resonance with a varying amplitude (˜18 kHz+/−60Hz, 120 Hz, 180 Hz . . . ) and to provide a ramp drive for the verticalmirror motion (60 Hz, 120 Hz, 180 Hz . . . ). The frequency responsecharacteristics of mirror 116 and gimbal 340 act to separate the torquecomponents into their respective motions.

The frequencies of the various resonant modes may vary based on selecteddesign criteria. For example, the frequency of the dominant resonantmode on the fast-scan axis may be increased or decreased by modifyingthe inertial mass of scanning mirror 116, or by varying properties offlexures 310 and 312. Likewise, the frequency of the dominant resonantmode on the slow-scan axis may be increased or decreased by modifyingthe properties of flexures 320 and 322, or by modifying the inertialmass of gimbal 340 and scanning mirror 116. An example MEMS mirror withdifferent resonant characteristics is described in Randall B. Sprague etal., Bi-axial Magnetic Drive for Scanned Beam Display Mirrors, Proc.SPIE, Vol. 5721, 1 (Jan. 24, 2005); DOI:10.1117/12.596942 OnlinePublication Date: 28 Feb. 2005. One skilled in art will appreciate thatany scanning mirror with any resonant properties may be utilized withthe various embodiments of the present invention.

The scanning mirror shown in FIG. 3 is an example of a “coil drivenmirror”, and more specifically, a “moving coil” design, because the coilmoves in the presence of a magnetic field. In other embodiments, themirror has one or more fixed magnets attached thereto, and the coil isstationary. In still further embodiments, other types of drivemechanisms are utilized (e.g., capacitively driven MEMS mirrors). Thetype of drive mechanism used to cause mirror motion is not a limitationof the present invention.

Scanning platform 114 is an example of a scanning mirror assembly thatscans light in two dimensions. In some embodiments the scanning mirrorassembly includes a single mirror that scans in two dimensions (e.g., ontwo axes). Alternatively, in some embodiments, scanning platform 114 maybe an assembly that includes two scan mirrors, one which deflects thebeam along one axis, and another which deflects the beam along a secondaxis largely perpendicular to the first axis. Either the first or secondscan mirror may be the fast-scan mirror or the slow-scan mirror.

Various embodiments of the present invention provide a feedback loopthat modifies the scanning mirror drive signals to produce the desiredscanning mirror behavior in the presence of high mechanical gain andnon-linear characteristics that produce additional motion distortion. Insome embodiments, the amplitude and phase of each of the harmonic drivesignals is modified in response to the measured behavior of the mirror.Further, each harmonic signal may be modified at a different rate (the“learning rate”). For example, harmonic signals in regions of highmechanical gain may be modified more slowly (have lower learning rates)than harmonic signals in regions of low mechanical gain.

FIG. 4 shows a scanning mirror fast-scan control loop with a fast-scanamplitude drive circuit. The fast-scan control loop includes fast-scanoscillation drive circuit 410, fast-scan amplitude drive circuit 420,multiplier 440, summer 450, and digital-to-analog converter 430.Scanning mirror 432 may be any scanning mirror that senses and providesan analog fast-scan position signal, including the examples describedabove with reference to FIG. 3. The remaining components depicted inFIG. 4 represent a scanning mirror control circuit, such as scanningmirror control circuit 130 (FIG. 1).

Scanning mirror 432 includes position sensors in the fast-scandirection. These sensors provide a signal that corresponds to the actualangular displacement of the mirror in the fast-scan direction. Theanalog fast-scan position signal is provided from the sensors to othercircuits on node 134. Scanning mirror 432 may be any suitable scanningmirror implementation, including a single axis scanning mirror or a dualaxis scanning mirror.

In operation, fast-scan oscillation drive circuit 410 receives theanalog fast-scan position signal on node 134 and produces a digitalsignal to excite a resonant mode of scanning mirror 432 on the fast-scanaxis. In some embodiments, this corresponds to generating a digitalfast-scan oscillation drive signal at substantially 18 kHz with asubstantially constant amplitude. Fast-scan amplitude drive circuit 420receives the analog fast-scan position signal on node 134 and produces adigital signal that modifies the amplitude of the sinusoidal oscillationof the scanning mirror as a function of time. The fast-scan oscillationdrive signal on node 411 and the fast-scan amplitude drive signal onnode 421 are multiplied together by multiplier 440 to produce thecomplete fast-scan drive signal on node 441. In single two-axis mirrorembodiments, the fast-scan drive signal on node 441 is summed with aslow-scan drive signal by summer 450 prior to being converted to ananalog drive signal by digital-to-analog converter 430 to drive scanningmirror 432. In single axis mirror embodiments, summer 450 is omitted.

As described in more detail below, various embodiments of fast-scanamplitude drive circuit 420 generate and sum digital harmonicallyrelated time domain signals to create the digital fast-scan amplitudedrive signal. Fast scan amplitude drive circuit 420 adaptively modifiesthe digital harmonically related time domain signals until the amplitudeof the fast-scan position signal matches a time-domain waveformspecified by harmonic coefficient targets specified as:T _(n) =T _(R) +iT _(I),  (1)

where n is the harmonic number, T _(n) is complex, T_(R) is the real,and iT_(I) is imaginary.

FIG. 5 shows a fast-scan oscillation drive circuit. Fast-scanoscillation drive circuit 500 is an example circuit that may perform thefunction of fast-scan oscillation drive circuit 410 (FIG. 4). Fast-scanoscillation drive circuit 500 includes analog comparator 510, phasedetector 520, proportional/integral/derivative (PID) controller 530,phase accumulator 540, digital comparator 570, summer 550, and sin wavegenerator 560.

In operation, analog comparator 510 compares the analog fast-scanposition signal with a static value, shown as “0” in FIG. 5. If theanalog fast-scan position signal varies positive and negative, then thecomparison value may be electrical ground. Any offset may be appliedwithin analog comparator 510 without departing from the scope of thepresent invention. The output of analog comparator 510 is a square waveat the fast-scan oscillation frequency, which in this example is shownas 18 kHz.

Phase detector 520 compares the output of analog comparator 510 with theoutput of digital comparator 570, and produces an error signal that ispresented to PID controller 530. PID controller 530 functions as a loopfilter to modify the phase increment that is accumulated by phaseaccumulator 540 as a function of the error signal. The variousembodiments of the present invention are not limited to the use of PIDcontrollers. Any suitable loop filter may be employed.

Digital comparator 570 compares the output of phase accumulator 540 witha static value to create a square wave at the same frequency as thefast-scan position signal, which in this example is 18 kHz. The staticcomparison value is shown as “0”, which corresponds to phase accumulator540 accumulating phase between negative 180 degrees and positive 180degrees. One skilled in the art will appreciate that any phase offsetwithin phase accumulator 540 may be paired with a suitable staticcomparison value to achieve the desired result.

Summer 550 sums a phase offset with the output of phase accumulator 540,and provides the result to sin wave generator 560. Sin wave generator560 is shown as implementing a CORDIC algorithm, although this is not alimitation of the present invention. For example, a look up table may beused to map phase values to sin values. The result is the fast-scanoscillation drive signal on node 411.

Fast-scan oscillation drive circuit 500 implements a digital phase lockloop to track the resonant frequency of the fast-scan mirror motion. Insome embodiments, an analog phase lock loop is employed.

FIG. 6 shows a fast-scan amplitude drive circuit. Fast-scan amplitudedrive circuit 600 is an example circuit that may perform the function offast-scan amplitude drive circuit 420 (FIG. 4). Fast-scan amplitudedrive circuit 600 includes harmonic tone generators 602, amplitudedetector 660, and least mean square (LMS) tone adders 610, 620, 630, and640, corresponding to one tone adder for each of n tones to be summed.

Amplitude detector 660 receives the analog fast-scan position signal onnode 134 and produces a digital fast-scan amplitude signal on node 662.This corresponds to receiving fast-scan deflection waveform 220 (FIG. 2)as an analog signal, and producing amplitude signal 222 (FIG. 2) as astream of digital samples. In some embodiments, amplitude detector 660may include an analog-to-digital converter and peak detector. In otherembodiments, amplitude detector 660 may include a comparator thatcompares the analog fast-scan position signal with a non-zero referencevalue. The resulting pulse width may then be mapped to an amplitudevalue. The digital fast-scan amplitude signal on node 662 is provided toeach of the LMS tone adders.

Harmonic tone generators 602 generate a number of harmonically relatedtones. The fast-scan amplitude drive signal on node 421 is constructedfrom weighted versions of tones at these frequencies. Multiples of 60 Hzare used in the example of FIG. 6; however this is not a limitation ofthe present invention.

LMS tone adder 610 (the first tone adder) receives a 60 Hz tone, thecorresponding coefficient T ₁, and the digital fast-scan amplitudesignal. LMS tone adder 620 (the second tone adder) receives a 120 Hztone, the corresponding coefficient T ₂, and the digital fast-scanamplitude signal. LMS tone adder 630 (the third tone adder) receives a180 Hz tone, the corresponding coefficient T ₃, and the digitalfast-scan amplitude signal. LMS tone adder 640 (the n^(th) tone adder)receives a 60 n Hz tone, the corresponding coefficient T _(n), and thedigital fast-scan amplitude signal. Summer 650 sums the harmonicallyrelated signals generated by the tone adders, and produces the digitalfast-scan amplitude drive signal.

In operation, each LMS tone adder compares a spectral component(harmonic of the fundamental) of the digital fast-scan amplitude signalagainst a target. The number of tone adders is equal to the number ofsignal harmonics in the fast-scan amplitude drive signal. Any number ofharmonics and any number of tone adders may be included withoutdeparting from the scope of the present invention. For example, in someembodiments, ten tone adders may be utilized, and the harmonics mayrange from 60 Hz to 600 Hz. In other embodiments, 17 tone adders may beutilized, and the harmonics may range from 60 Hz to 1.02 kHz. The numberof harmonics utilized represents a tradeoff between drive signalfidelity and implementation complexity.

The example of FIG. 6 shows a fundamental frequency of 60 Hz andharmonics thereof, although the various embodiments of the invention arenot so limited. For example, a sawtooth fast-scan amplitude deflectionmay have a fundamental frequency other than 60 Hz, in which case theharmonic tones will be at frequencies other than at multiples of 60 Hz.Also for example, the fast-scan amplitude trajectory may be any signalthat may be constructed from a sum of sinusoids.

FIG. 7 shows an LMS tone adder. LMS tone adder 610 includes in-phase andquadrature circuits to operate on complex signal samples. The in-phasecircuit includes summers 714 and 730, multipliers 710 and 732, low passfilter (LPF) 712, and a proportional/integral/derivative (PID)controller that includes a proportional block (P), an integrator block(I), and a derivative block (D). The quadrature circuit includes summers764 and 780, multipliers 760 and 782, low pass filter (LPF) 762, and aproportional/integral/derivative (PID) controller that includes aproportional block (P), an integrator block (I), and a derivative block(D). The outputs of the in-phase and quadrature channels are combined bysummer 790 to create the harmonic output signal. FIG. 7 shows the firstLMS tone adder of FIG. 6 (610). This tone adder receives a 60 Hz toneand the coefficient for the 60 Hz target, and produces the 60 Hz drivesignal. Other LMS tone adders include identical functional blocks, butreceive tones and targets for different harmonics.

In operation, multipliers 710 and 760 mix the fast-scan amplitude signalwith in-phase and quadrature components of a 60 Hz tone, translating thesignal spectrum at 60 Hz to DC. Phase information is preserved throughthe quadrature operation. Low pass filters 712 and 762 remove spectralenergy corresponding to harmonics that were not translated to DC. Forexample, the cutoff frequency of low pass filters 712 and 762 may beabout 20 Hz. The DC output of filters 712 and 762 represents theharmonic coefficient R _(k) that is “returned” from the scanning mirror.The return harmonic coefficients are represented asR _(n) =R _(R) +iR _(I)  (2)

where n is the harmonic number, R _(n) is complex, R_(R) is real, andiR_(I) is imaginary. These DC values are compared with (subtracted from)the target values, with the differences being the error signals whichare applied to the PID controllers. The PID controllers operate to drivethe in-phase and quadrature errors to zero. The output of the PID blocksare summed at 730 and 780 to form a complex harmonic drive coefficientrepresented asD _(n) =D _(R) +iD _(I),  (3)

where n is the harmonic number, D _(n) is complex, D_(R) is real, andiD_(I) is imaginary. The harmonic drive coefficient is mixed back up to60 Hz by multipliers 732 and 782 to generate the in-phase and quadraturecomponents of the 60 Hz drive signal, which are combined at 790.

In some embodiments, LMS tone adder 610 does not utilize theproportional blocks (P) or the derivative blocks (D). In theseembodiments, the integrator blocks (I) integrate the error terms toarrive at the output signals.

FIG. 8 shows a fast-scan amplitude drive circuit using a harmoniccoefficient weighting array. Fast-scan amplitude drive circuit 800 is anexample circuit that may perform the function of fast-scan amplitudedrive circuit 420 (FIG. 4). Fast-scan amplitude drive circuit 800includes harmonic tone generators 602, amplitude detector 660, and LMStone adders 810, 820, 830, and 840, and summer 650. Harmonic tonegenerators 602, amplitude detector 660, and summer 650 are describedabove with reference to FIG. 6. LMS tone adders 810, 820, 830, and 840correspond to the LMS tone adders of FIG. 6 except that LMS tone adders810, 820, 830, and 840 receive a harmonic coefficient weighting arrayα_(k).

Similar to fast-scan amplitude drive circuit 600 in FIG. 6, fast-scanamplitude drive circuit 800 receives the analog fast-scan positionsignal and harmonic coefficient targets, T _(n), and produces a digitalfast-scan amplitude drive signal. Fast-scan amplitude drive circuit 800differs from fast-scan amplitude drive circuit 600, in that circuit 800also receives a harmonic coefficient weighting array to providedifferent “learning rates” for each harmonic coefficient. Alpha, α_(k),is the weighting array that provides appropriate magnitude and phasescaling (vector direction) for successive reduction of the errorquantity.

In some embodiments, the weighting array is the inverse of the mirrorgain (transfer function) normalized to one at the primary frequency (60Hz). One or more mirrors can be characterized, and the weighting arrayis determined from the measured transfer function. Alternatively, thelinear transfer function of the mirror can be measured and learned atdevice startup or during operation of the device. For example, assumethat a measured mirror gain (see FIG. 6) at 60 Hz intervals for 17harmonics is as follows:

-   -   MirrorGain=[0.0562, 0.0595, 0.0630, 0.0653, 0.0668, 0.0724        0.0812, 0.0912, 0.1122, 0.1496, 0.2511, 1.0, 1.0, 0.2511 0.1412,        0.0944, 0.0668]

where the first entry of MirrorGain corresponds to the gain at 60 Hz andthe last entry of Mirror Gain corresponds to the gain at 1.02 kHz. Theseare shown as real coefficients (magnitude only), but they can be complexvalues (magnitude and phase). The weighting array α_(k) (Alpha(k)) canbe determined using the following algorithm:

$\mspace{20mu}{{{Alpha}^{\prime}(k)} = {\frac{{MirrorGain}(k)}{{MirrorGain}(1)}//{{Normalize}\mspace{14mu}{to}\mspace{14mu}{the}\mspace{14mu}{first}\mspace{14mu}{harmonic}}}}$$\alpha_{k} = {\frac{1}{{Alpha}^{\prime}(k)}//{{Inverse}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{linear}\mspace{14mu}{gain}\mspace{14mu}{at}\mspace{14mu}{each}\mspace{14mu}{discrete}\mspace{14mu}{harmonic}\mspace{14mu}({frequency})}}$

It should be noted that the Alpha weighting does not necessarily have toconform to the MEMS gain properties. The MEMS transfer function can bemodified by a closed loop feedback system and the composite gain of thecombined system can be used to compute α_(k) (Alpha(k)).

FIG. 9 shows an LMS tone adder using harmonic coefficient weighting. LMStone adder 810 includes all of the components shown in FIG. 7. Inaddition, LMS tone adder 810 shows coefficient weighting blocks 910 and920. Coefficient weighting blocks 910 and 920 provide scaling to theerror signal, thereby allowing each LMS tone adder to have a differentlearning rate for the corresponding drive coefficient.

FIG. 10 shows a fast-scan amplitude drive circuit that iterativelydetermines harmonic coefficients using a harmonic coefficient weightingarray. Fast-scan amplitude drive circuit 1000 is an example circuit thatmay perform the function of fast-scan amplitude drive circuit 420 (FIG.4). Fast-scan amplitude drive circuit 1000 includes iterative harmoniccoefficient determination block 1010, amplitude detector 660, summingbuffer 1060, fast Fourier transform (FFT) block 1070, and inverse fastFourier transform (IFFT) block 1012.

In operation, iterative harmonic coefficient determination blockdetermines harmonic drive coefficients represented asD _(n) =D _(R) +iD _(I),

where n is the harmonic number, D _(n) is complex, D_(R) is real, andiD_(I) is imaginary. See equation (3), above. Inverse fast Fouriertransform (IFFT) block 1012 produces a time domain fast-scan amplitudedrive signal from the harmonic drive coefficients.

Amplitude detector 660 receives the analog fast-scan position signal onnode 134 and produces a digital fast-scan amplitude signal. Amplitudedetector 660 is further described above with reference to FIG. 6.Summing buffer 1060 sums (or averages) the fast-scan amplitude waveformover N cycles to increase the signal-to-noise ration (SNR). Thefast-scan amplitude waveform can be averaged over any number of cycleswithout departing from the scope of the present invention. The averagedfast-scan amplitude waveform is processed by FFT 1070 to yield thereturn harmonic coefficients represented asR _(n) =R _(R) +iR _(I),

where n is the harmonic number, R _(n) is complex, R_(R) is real, andiR_(I) is imaginary. See equation (2), above. Iterative harmoniccoefficient determination block 1010 receives the return harmoniccoefficients R _(n) as well as harmonic coefficient targets and aharmonic coefficient weighting array α_(n). The harmonic coefficienttargets are represented asT _(n) =T _(R) +iT _(I),

where n is the harmonic number, T _(n) is complex, T_(R) is the real,and iT_(I) is imaginary. See equation (1), above. Iterative harmoniccoefficient determination block 1010 determines the error in the returncoefficients asĒ _(n) = T _(n) − R _(n),  (4)

and then updates the harmonic drive coefficients asD _(n) ^(k+1) = D _(n) ^(k)+βα_(n) Ē _(n) ^(k),  (5)where the superscript k in equation (5) refers the k^(th) iteration, thek+1 superscript refers to the next iteration, β is a global gain value(learning rate) in the range of 0 to 1. Alpha, α_(n), is the staticweighting array that provides appropriate magnitude and phase scaling(vector direction) for successive reduction of the error quantity E_(n).

In some embodiments, the weighting array is the inverse of the mirrorgain (transfer function) normalized to one at the primary frequency (60Hz). One or more mirrors can be characterized, and the weighting arrayis determined from the measured transfer function. Alternatively, thelinear transfer function of the mirror can be measured and learned atdevice startup or during operation of the device. For example, assumethat a measured mirror gain at 60 Hz intervals for 17 harmonics is asfollows:

-   -   MirrorGain=[0.0562, 0.0595, 0.0630, 0.0653, 0.0668, 0.0724        0.0812, 0.0912, 0.1122, 0.1496, 0.2511, 1.0, 1.0, 0.2511 0.1412,        0.0944, 0.0668]

where the first entry of MirrorGain corresponds to the gain at 60 Hz andthe last entry of Mirror Gain corresponds to the gain at 1.02 kHz. Theseare shown as real coefficients (magnitude only), but they can be complexvalues (magnitude and phase). The weighting array α_(n) (Alpha(n)) canbe determined using the following algorithm:

$\mspace{20mu}{{{Alpha}^{\prime}(n)} = {\frac{{MirrorGain}(n)}{{MirrorGain}(1)}//{{Normalize}\mspace{14mu}{to}\mspace{14mu}{the}\mspace{14mu}{first}\mspace{14mu}{harmonic}}}}$$\alpha_{n} = {\frac{1}{{Alpha}^{\prime}(n)}//{{Inverse}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{linear}\mspace{14mu}{gain}\mspace{14mu}{at}\mspace{14mu}{each}\mspace{14mu}{discrete}\mspace{14mu}{harmonic}\mspace{14mu}({frequency})}}$

It should be noted that the Alpha weighting does not necessarily have toconform to the MEMS gain properties. The MEMS transfer function can bemodified by a closed loop feedback system and the composite gain of thecombined system can be used to compute α_(n) (Alpha(n)).

The harmonic drive coefficient update shown in equation (5) and theoperation of IFFT 1012 can be performed in accordance with the followingpseudocode, where Return(n) is R _(n) ^(k), Dold(n) is D _(n) ^(k),Dnew(n) is D _(n) ^(k+1), Targ(n) is T _(n), and Timepts is an integercorresponding to the number of points in the ramp waveform:

Loop until ramp is smooth (linear) // Main Loop forn=1:num_tune_harmonics // 17 harmonics in this example Dnew(n)=Dold(n) +(Beta*Alpha(n)*(Targ(n)−Return(n))); // Primary iterative equation (5)end for DnewAmp=abs(Dnew); // absolute value of each drive coefficientDnewphz=atan(imag(Dnew),real(Dnew)); // phase of each drive coefficientFor tt=1:(timepts); // Construct time domain ramp from new coefficientstime(tt)=tt/(timepts; //normalized to one period Votemp=0; forn=1:num_tune_harmonics //sum of harmonics in time domainVotemp=Votemp+(DnewAmp(n)*sin((n*w*time(tt))+Dnewphz(n))); end forVo(tt)=Votemp; end for Voltdrive=Vo; //array of time domain Ramp DriveDold=Dnew end loop // Main Loop

FIG. 11 shows a fast-scan amplitude drive circuit that iterativelydetermines harmonic coefficients using an approximation of Newton'smethod. Fast-scan amplitude drive circuit 1100 is an example circuitthat may perform the function of fast-scan amplitude drive circuit 420(FIG. 4). Fast-scan amplitude drive circuit 1100 includes amplitudedetector 660, summing buffer 1060, fast Fourier transform (FFT) block1070, and inverse fast Fourier transform (IFFT) block 1012, all of whichare described above with respect to FIG. 10.

Fast-scan amplitude drive circuit 1100 also includes Newton's methodharmonic coefficient determination block 1110. Similar to block 1010 inFIG. 10, block 1110 receives the return harmonic coefficients R _(n) andtargets T _(n), and produces harmonic drive coefficients D _(n). TheNewton's method block 1110 differs from block 1010, in that block 1110does not receive a weighting array. Instead, block 1110 adaptivelymodifies the learning rate of each harmonic coefficient as explainedbelow.

In numerical analysis, Newton's method is useful for findingsuccessively better approximations to the zeros (or roots) of areal-valued function. As applied to the current problem, Newton's methodcan be shown as:

$\begin{matrix}{{\overset{\_}{D}}_{n}^{k + 1} = {{\overset{\_}{D}}_{n}^{k} - {\lbrack \frac{\mathbb{d}{\overset{\_}{E}}_{n}^{k}}{\mathbb{d}{\overset{\_}{D}}_{n}^{k}} \rbrack^{- 1}{{\overset{\_}{E}}_{n}^{k}.}}}} & (6)\end{matrix}$

A discrete approximation to Newton's method as applied to the currentproblem can be shown as

$\begin{matrix}{{{\overset{\_}{D}}_{n}^{k + 1} \approx {{\overset{\_}{D}}_{n}^{k} + {\lbrack \frac{{\overset{\_}{D}}_{n}^{k} - {\overset{\_}{D}}_{n}^{k - 1}}{{\overset{\_}{R}}_{n}^{k} - {\overset{\_}{R}}_{n}^{k - 1}} \rbrack{\overset{\_}{E}}_{n}^{k}}}},} & (7)\end{matrix}$

where ΔD_(n) ^(k)= D _(n) ^(k)− D _(n) ^(k−1) represents the change indrive on previous iteration, and

$\begin{matrix}{G_{n}^{k} = \lbrack \frac{{\overset{\_}{D}}_{n}^{k} - {\overset{\_}{D}}_{n}^{k - 1}}{{\overset{\_}{R}}_{n}^{k} - {\overset{\_}{R}}_{n}^{k - 1}} \rbrack} & (8)\end{matrix}$

represents the gain (weighting) on the k^(th) iteration for n^(th)harmonic. Note that G_(n) ^(k) in equation 7 takes the place of α_(n)(Alpha) in equation (5), and also that G_(n) ^(k) is a function of theprevious changes in drive coefficients as well as previous changes inreturn coefficients. Accordingly, the weighting for each harmoniccoefficient is adaptive in embodiments represented by FIG. 11, whereasthe weighting for each harmonic coefficient is fixed in embodimentsrepresented by FIG. 10. In some embodiments, both the fixed Alpha valuesand G_(n) ^(k) are used to compute new weighting coefficients at eachiteration.

The following algorithm demonstrates use of the discrete approximationof Newton's method during each iteration:

for n=num_tune_harmonics //shift phase of each harmonic so that drivewaveform is in phase with return${\overset{\_}{R}}_{n}^{k} = {{\overset{\_}{R}}_{n}^{k}{\mathbb{e}}^{{\mathbb{i}}{({\phi_{D}^{{n = 0},k} - \phi_{R}^{{n = 0},k}})}}}$//compute error and magnitude of error Ē_(n) ^(k) = T _(n) ^(k) − R _(n)^(k)${{\overset{\_}{E}}_{n}^{k}} = \sqrt{{\overset{\_}{E}}_{n}^{k}{\overset{\_}{E}}_{n}^{k^{*}}}$//compute magnitude of return and old delta D${{\overset{\_}{R}}_{n}^{k}} = \sqrt{{\overset{\_}{R}}_{n}^{k}{\overset{\_}{R}}_{n}^{k^{*}}}$${{\Delta D}_{n}^{k}} = \sqrt{{\Delta D}_{n}^{k}{\Delta D}_{n}^{k^{*}}}$if error is less than one bit  //error has converged, so set delta driveto zero and  //set the new gain to the old gain  ΔD_(n) ^(k+1) = 0 G_(n) ^(k+1) = G_(n) ^(k) else if the old delta drive is zero and theerror is large  //use the stored gain to update the new drive  ΔD_(n)^(k+1) = G_(n) ^(k)E_(n) ^(k)  D_(n) ^(k+1) = D_(n) ^(k) + ΔD_(n) ^(k+1) G_(n) ^(k+1) = G_(n) ^(k) else if the old delta drive is not zero andthe return is zero  //increase the old drive by a factor of two andstore the old gain  coefficient  ΔD_(n) ^(k+1) = 2D_(n) ^(k)  D_(n)^(k+1) = D_(n) ^(k) + ΔD_(n) ^(k+1)  G_(n) ^(k+1) = G_(n) ^(k) Else //no exceptions, so perform the Newton's iteration$G_{n}^{k + 1} = \frac{D_{n}^{k} - D_{n}^{k - 1}}{R_{n}^{k} - R_{n}^{k - 1}}$ ΔD_(n) ^(k+1) = G_(n) ^(k+1)E_(n) ^(k)  D_(n) ^(k+1) = D_(n) ^(k) +ΔD_(n) ^(k+1) end for

Iterations may be performed on a periodic basis. For example, thealgorithm above may be performed once per second or once per manyseconds.

FIG. 12 shows a scanning mirror fast-scan control loop with a fast-scansideband generator circuit. The fast-scan control loop shown in FIG. 12is similar to that shown in FIG. 4 with the exception of fast-scansideband generator 1220 and summer 1240. In operation, fast-scansideband generator 1220 generates a fast-scan sideband drive signal onnode 1221 that corresponds to the sidebands present on the drive signalto achieve the desired amplitude drive. Summer 1240 sums the fast-scanoscillation drive signal on node 411 with the fast-scan sideband drivesignal on node 1221 to produce the fast-scan drive signal on node 441.Fast-scan sideband generator 1220 receives the harmonic coefficienttargets, T _(n), which in this case represent the targets for the signalsidebands. In operation, fast-scan sideband generator 1220 modifies thefast-scan sideband drive signal on node 1221 until the sidebands presentin the analog fast-scan position signal closely match the sidebandsspecified by the harmonic coefficient targets, T _(n).

FIG. 13 shows a fast-scan sideband generator. Fast-scan sidebandgenerator 1300 is an example circuit that may perform the function offast-scan amplitude drive circuit 1220 (FIG. 12). Fast-scan sidebandgenerator 1300 includes tone generators 1302, analog-to-digitalconverter (ADC) 1360, and LMS tone adders 1310, 1320, 1330, and 1340,corresponding to one tone adder for each of n tones to be summed.

ADC 1360 receives the analog fast-scan position signal on node 134 andproduces a digital fast-scan position signal on node 1362. The digitalfast-scan position signal on node 1362 is provided to each of the LMStone adders. This is in contrast to the circuits shown in FIGS. 6 and 8in which each of the LMS tone adders receives a digital fast-scanamplitude signal.

Tone generators 1302 generate a number of tones related to the fast scanresonant frequency. The fast-scan sideband drive signal on node 1221 isconstructed from weighted versions of tones at these frequencies. Thesidebands are centered at the fast-scan resonant frequency (18 kHz inthis example), and are multiples of the fundamental frequency of thefast-scan amplitude signal (60 Hz in this example). Accordingly,harmonic tone generators 1302 produce tones at 18 kHz+/60 Hz, 18kHz+/120 Hz, 18 kHz+/180 Hz, etc.

LMS tone adder 1310 (the first tone adder) receives a 18.060 kHz tone,the corresponding coefficient T ₁, and the digital fast-scan positionsignal. LMS tone adder 1320 (the second tone adder) receives a 18.120kHz tone, the corresponding coefficient T ₂, and the digital fast-scanposition signal. LMS tone adder 1330 (the third tone adder) receives a18.180 kHz tone, the corresponding coefficient T ₃, and the digitalfast-scan position signal. LMS tone adder 1340 (the n^(th) tone adder)receives a 60 n Hz tone, the corresponding coefficient T _(n), and thedigital fast-scan position signal. Summer 1350 sums the signalsgenerated by the tone adders, and produces the digital fast-scanamplitude drive signal. For simplicity, FIG. 13 only shows LMS toneadder receiving the upper side bands. In practice, an equal number ofadditional LMS tone adders are present receiving the corresponding lowersidebands. Summer 1350 sums both the lower and upper sidebands whenproducing the fast-scan sideband drive signal on nod 1221.

In operation, each LMS tone adder compares a sideband of the fast-scanposition signal against a target. The number of tone adders is equal tothe number of sidebands processed when generating the fast-scan sidebanddrive signal. Any number of sidebands and any number of tone adders maybe included without departing from the scope of the present invention.For example, in some embodiments, ten tone adders may be utilized, andthe sidebands may range from 17.700 kHz to 18.300 kHz. In otherembodiments, more tone adders may be utilized. The number of sidebandsutilized represents a tradeoff between drive signal fidelity andimplementation complexity.

The example of FIG. 13 shows sidebands at harmonics of 60 Hz, althoughthe various embodiments of the invention are not so limited. Forexample, a sawtooth fast-scan amplitude deflection may have afundamental frequency other than 60 Hz, in which case the sidebands willbe at frequencies other than at multiples of 60 Hz.

Each of LMS tone adders 1310, 1320, 1330, and 1340 may be implemented asany of the previously described tone adders. For example, the toneadders may be implemented as tone adder 610 (FIG. 7), or tone adder 810(FIG. 9).

The functional blocks shown in FIGS. 4-13 may be implemented in anymanner without departing from the scope of the present invention. Forexample, any combination of hardware and/or software may be utilized, aswell as any level of integration. In some embodiments, a completehardware solution is implemented. For example, one or more applicationspecific integrated circuits (ASIC) or field programmable gate arrays(FPGA) may implement most or all of the blocks shown.

In other embodiments, a processor executes instructions to perform theactions associated with FIGS. 4-13. For example, a digital signalprocessor (DSP) may be employed. FIG. 14 shows a fast-scan control loopthat includes a digital signal processor (DSP), memory 1420 ADC 1460,DAC 1430, low pass filters 1440 and 1450, and scanning mirror 432. DSP1410 may be any type of processor capable of performing the actionsdescribed herein. For example, DSP 1410 may be a commercially availableprocessor or may be a custom processor. Further, DSP 1410 may be astandalone integrated circuit or may be a “core” that is included in anASIC.

DSP 1410 receives digitized samples from ADC 1460 and provides digitaldata for fast-scan drive signal to DAC 1430. In dual axis mirrorembodiments, the fast-scan drive signal is first summed with theslow-scan drive signal at summer 450. In some embodiments, DSP 1410performs the LMS harmonic control functions according to the embodimentsshown in FIG. 6, 8, or 13. Specifically, DSP 1410 may or may not use afixed weighting array to provide different learning rates for eachharmonic coefficient, where each harmonic coefficient represents eithera component of an amplitude drive signal or a component of a sidebanddrive signal. In other embodiments, DSP 1410 also performs the fast-scanoscillation drive functions shown in, and described with reference to,FIGS. 4, 5, and 12.

Memory 1320 is a computer-readable medium upon which instructions arestored. For example, memory 1420 may be a volatile memory such as staticor dynamic random access memory (SRAM or DRAM) or may be non-volatilememory such as FLASH memory. In some embodiments, DSP 1410 and memory1420 are included in a common integrated circuit such as an ASIC. Memory1420 may also be a medium suitable for distribution such as disk (hard,soft, compact, or otherwise) or server with downloadable files.

DSP 1410 accesses instructions from memory 1420 and performs variousmethod embodiments of the present invention. For example, any of the LMSharmonic control embodiments may be performed by DSP 1410. In addition,DSP 1410 may characterize the response of scanning mirror 732 asdescribed above with reference to the MirrorGain array.

Although DSP 1410 is shown only generating the fast scan drive signals,this is not a limitation of the present invention. For example, in someembodiments, DSP 1410 determines the slow scan and fast scan drivesignals and sums them internally.

FIG. 15 shows a block diagram of a mobile device in accordance withvarious embodiments of the present invention. As shown in FIG. 15,mobile device 1500 includes wireless interface 1510, processor 1520,memory 1530, and scanning projector 1501. Scanning projector 1501 may beany of the projection embodiments described with reference to previousfigures. For example, scanning projector 1501 may be a scanningprojector with a non-uniform scan angle amplitude in the fast-scandimension. In some embodiments, scanning projector 1501 includes LMStone adders, or iterative circuitry to learn harmonic coefficients thatproduce the desired fast-scan amplitude variations.

Scanning projector 1501 may receive image data from any image source.For example, in some embodiments, scanning projector 1501 includesmemory that holds still images. In other embodiments, scanning projector1501 includes memory that includes video images. In still furtherembodiments, scanning projector 1501 displays imagery received fromexternal sources such as connectors, wireless interface 1510, or thelike.

Wireless interface 1510 may include any wireless transmission and/orreception capabilities. For example, in some embodiments, wirelessinterface 1510 includes a network interface card (NIC) capable ofcommunicating over a wireless network. Also for example, in someembodiments, wireless interface 1510 may include cellular telephonecapabilities. In still further embodiments, wireless interface 1510 mayinclude a global positioning system (GPS) receiver. One skilled in theart will understand that wireless interface 1510 may include any type ofwireless communications capability without departing from the scope ofthe present invention.

Processor 1520 may be any type of processor capable of communicatingwith the various components in mobile device 1500. For example,processor 1520 may be an embedded processor available from applicationspecific integrated circuit (ASIC) vendors, or may be a commerciallyavailable microprocessor. In some embodiments, processor 1520 providesimage or video data to scanning projector 1501. The image or video datamay be retrieved from wireless interface 1510 or may be derived fromdata retrieved from wireless interface 1510. For example, throughprocessor 1520, scanning projector 1501 may display images or videoreceived directly from wireless interface 1510. Also for example,processor 1520 may provide overlays to add to images and/or videoreceived from wireless interface 1510, or may alter stored imagery basedon data received from wireless interface 1510 (e.g., modifying a mapdisplay in GPS embodiments in which wireless interface 1510 provideslocation coordinates).

FIG. 16 shows a mobile device in accordance with various embodiments ofthe present invention. Mobile device 1600 may be a hand held projectiondevice with or without communications ability. For example, in someembodiments, mobile device 1600 may be a handheld projector with littleor no other capabilities. Also for example, in some embodiments, mobiledevice 1600 may be a device usable for communications, including forexample, a cellular phone, a smart phone, a personal digital assistant(PDA), a global positioning system (GPS) receiver, or the like. Further,mobile device 1600 may be connected to a larger network via a wireless(e.g., WiMax) or cellular connection, or this device can accept datamessages or video content via an unregulated spectrum (e.g., WiFi)connection.

Mobile device 1600 includes scanning projector 1501 to create an imageat 1580 as shown in FIG. 16. Image 1580 may be trapezoidal in shape dueto the varying fast-scan amplitude as described above. Mobile device1600 also includes many other types of circuitry; however, they areintentionally omitted from FIG. 16 for clarity.

Mobile device 1600 includes display 1610, keypad 1620, audio port 1602,control buttons 1604, card slot 1606, and audio/video (A/V) port 1608.None of these elements are essential. For example, mobile device 1600may only include scanning projector 1501 without any of display 1610,keypad 1620, audio port 1602, control buttons 1604, card slot 1606, orA/V port 1608. Some embodiments include a subset of these elements. Forexample, an accessory projector product may include scanning projector1501, control buttons 1604 and A/V port 1608.

Display 1610 may be any type of display. For example, in someembodiments, display 1610 includes a liquid crystal display (LCD)screen. Display 1610 may always display the same content as thatprojected or different content. For example, an accessory projectorproduct may always display the same content, whereas a mobile phoneembodiment may project one type of content while displaying differentcontent on display 1610. Keypad 1620 may be a phone keypad or any othertype of keypad.

A/V port 1608 accepts and/or transmits video and/or audio signals. Forexample, A/V port 1608 may be a digital port that accepts a cablesuitable to carry digital audio and video data, such as a highdefinition media interface (HDMI) interface. Further, A/V port 1608 mayinclude RCA jacks to accept composite inputs. Still further, A/V port1608 may include a VGA connector to accept analog video signals. In someembodiments, mobile device 1600 may be tethered to an external signalsource through A/V port 1608, and mobile device 1600 may project contentaccepted through A/V port 1608. In other embodiments, mobile device 1600may be an originator of content, and A/V port 1608 is used to transmitcontent to a different device.

Audio port 1602 provides audio signals. For example, in someembodiments, mobile device 1600 is a media player that can store andplay audio and video. In these embodiments, the video may be projectedand the audio may be output at audio port 1602. In other embodiments,mobile device 1600 may be an accessory projector that receives audio andvideo at A/V port 1608. In these embodiments, mobile device 1600 mayproject the video content, and output the audio content at audio port1602.

Mobile device 1600 also includes card slot 1606. In some embodiments, amemory card inserted in card slot 1606 may provide a source for audio tobe output at audio port 1602 and/or video data to be projected. Cardslot 1606 may receive any type of solid state memory device, includingfor example, Multimedia Memory Cards (MMCs), Memory Stick DUOS, securedigital (SD) memory cards, and Smart Media cards. The foregoing list ismeant to be exemplary, and not exhaustive.

In some embodiments, the user interface components shown in FIG. 16allow a user to specify characteristics of the fast-scan amplitudevariations. For example, display 1610 may show a menu item that allows auser to select a trapezoidal projected display shape at 1580, and bydoing so, mobile device modifies the harmonic coefficient targets, T_(n).

FIG. 17 shows a head-up display system in accordance with variousembodiments of the invention. Projector 1501 is shown mounted in avehicle dash to project the head-up display at 1700. Although anautomotive head-up display is shown in FIG. 17, this is not a limitationof the present invention. For example, various embodiments of theinvention include head-up displays in avionics application, air trafficcontrol applications, and other applications. The non-rectangulardisplay shape capability of projector 1501 may allow the projecteddisplay to be pre-distorted to overcome any undesirable visual effectsresulting from projecting on a non-uniform windshield surface.

FIG. 18 shows eyewear in accordance with various embodiments of theinvention. Eyewear 1800 includes projector 1501 to project a display inthe eyewear's field of view. In some embodiments, eyewear 1800 issee-through and in other embodiments, eyewear 1800 is opaque. Forexample, eyewear may be used in an augmented reality application inwhich a wearer can see the display from projector 1501 overlaid on thephysical world. Also for example, eyewear may be used in a virtualreality application, in which a wearer's entire view is generated byprojector 100. Although only one projector 1501 is shown in FIG. 18,this is not a limitation of the present invention. For example, in someembodiments, eyewear 1800 includes two projectors; one for each eye. Thenon-rectangular display shape capability of projector 1501 may allow theprojected display to be pre-distorted to overcome any undesirable visualeffects resulting from projecting on a non-uniform eyewear surface.

Although the present invention has been described in conjunction withcertain embodiments, it is to be understood that modifications andvariations may be resorted to without departing from the scope of theinvention as those skilled in the art readily understand. Suchmodifications and variations are considered to be within the scope ofthe invention and the appended claims.

What is claimed is:
 1. An apparatus comprising: a scanning mirror havinga fast-scan axis and a slow-scan axis, the fast-scan axis having aposition detector to provide an analog fast-scan position signal thatcorresponds to an angular displacement of the scanning mirror on thefast-scan axis; and a control loop coupled to be responsive to theanalog fast-scan position signal, the control loop configured to modifya scanning mirror drive signal to produce a non-uniform fast-scanamplitude across each sweep on the slow-scan axis; wherein the controlloop includes: an amplitude detector that includes a peak detector todetect an amplitude of the analog fast-scan position signal and producea digital amplitude signal; and a plurality of least mean square (LMS)tone adders to determine harmonically related components of a fast-scanamplitude drive signal in response to the digital amplitude signal. 2.The apparatus of claim 1 wherein the control loop is configured tomodify the scanning mirror drive signal to produce a trapezoidal displayshape.
 3. The apparatus of claim 1 wherein the plurality of LMS toneadders operate to modify the harmonically related components of thefast-scan amplitude drive signal at different rates.
 4. The apparatus ofclaim 1 wherein each of the LMS tone adders comprises a multiplier tomultiply the digital amplitude signal with a tone at a harmonicfrequency.
 5. The apparatus of claim 4 wherein each of the LMS toneadders further comprises a summer to compare a harmonic coefficienttarget with an output of the multiplier.
 6. The apparatus of claim 1wherein the control loop further includes a fast-scan oscillation drivecircuit to produce a fast-scan oscillation drive signal at a resonantfrequency of the fast-scan axis.
 7. The apparatus of claim 6 wherein thefast scan oscillation drive circuit comprises a phase lock loop circuitresponsive to the analog fast-scan position signal.
 8. The apparatus ofclaim 6 wherein the fast-scan oscillation drive circuit is configured toproduce the fast-scan oscillation drive signal at substantially 18 kHz.9. The apparatus of claim 6 further comprising a multiplier to combinethe fast-scan oscillation drive signal and the fast-scan amplitude drivesignal.
 10. A projection apparatus comprising: a resonant scanningmirror with at least one position sensor to sense an angulardisplacement of the resonant scanning mirror on a fast-scan axis, and toproduce an oscilating position signal; an amplitude detector including apeak detector to detect an amplitude of the oscillating position signalproduced by the at least one position sensor; and a control loop tomodify a scanning mirror drive signal to cause the amplitude of theoscillating position signal to vary substantially linearly for a finitetime period, wherein the control loop comprises a plurality of leastmean square (LMS) tone adders to determine harmonically relatedcomponents of an amplitude drive signal in response to the amplitude ofthe oscillating position signal.
 11. The projection apparatus of claim10 wherein the resonant scanning mirror comprises a dual axis scanningmirror.
 12. The projection apparatus of claim 11 wherein the controlloop modifies the scanning mirror drive signal to create a trapezoidaldisplay.